\iffalse

INSTRUCTIONS: (if this is not ps1, use the right file name)

  Clip out the ********* INSERT HERE ********* bits below and insert
appropriate TeX code.  Once you are done with your file, run

  ``latex template.tex''

from the Athena shell.  If your TeX code is clean, the latex will exit
back to a prompt.  Once this is done, run

  ``dvips template.dvi -o template.ps''

which should print your file to the nearest printer.  There will be
residual files called ps1.log, ps1.aux, and ps1.dvi.  All these can be
deleted, but do not delete ps1.tex.

\fi
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\newcommand{\handout}[5]{
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   \framebox{
      \vbox{
    \hbox to 5.78in { {\bf 6.001 SICP Spring 2004} \hfill #2 }
       \vspace{4mm}
       \hbox to 5.78in { {\Large \hfill #5  \hfill} }
       \vspace{2mm}
       \hbox to 5.78in { {\it #3 \hfill #4} }
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\newcommand{\ho}[5]{\handout{#1}{#2}{Instructor:
#3}{Teaching Assistant: #4}{Handout #1: #5}}
\newcommand{\al}{\alpha}
\newcommand{\Z}{\mathbb Z}

\begin{document}
\handout{P1}{3/15/2004}
{} % {Problem Set 4}
{} % {Instructor: foo}
{Tutorial 6} %{Bryan Russell}

\section*{Topics}
Tagged Data and Tables

\section*{Upcoming Deadlines}

\begin{itemize}
\item Problem set 5 due Tuesday, 3/16 at midnight
\item Lecture 12 due Wednesday, 3/17 at 9am
\item Lecture 13 LIVE on Thursday, 3/18 at 10am
\item Project 3 due Friday, 3/19 at 6pm
\item Reminder: my office hours are Wednesdays from 3-5pm
\item Next week is spring break (no office hours)
\end{itemize}

\section*{Tables - Binary Tree Implementation}

Some constructors, accessors, and predicates:

\begin{verbatim}
(define (make-empty-node) nil)
(define empty-node? null?)
(define node-tag 'node)
(define (make-node key val)
  (list node-tag key val (make-empty-node) (make-empty-node)))
(define (node? n)
  (and (pair? n) (eq? (car n) node-tag)))
(define get-key cadr)
(define get-val caddr)
(define get-left cadddr)
(define get-right caddddr)
(define (put! node val)
  (set-car! (cdr node) val) node)
(define (put-left! node left-node)
  (set-car! (cdddr node) left-node) node)
(define (put-right! node right-node)
  (set-car! (cddddr node) right-node) node)

(define table-tag 'table)
; comp-proc is a procedure that compares two values x and y.  If 
; (= x y) is true, comp-proc returns 0.  If (< x y) is true, then 
; comp-proc returns -1.  Else, it returns 1.
(define (make-table comp-proc) 
  (list table-tag comp-proc (make-empty-node)))
\end{verbatim}

\subsection*{Exercise 1}
Write the procedure ${\verb+table-get+}$ that gets the value
associated with a ${\verb+key+}$.

\begin{verbatim}
(define (table-get tbl key)
  EXERCISE-1)
\end{verbatim}

\subsection*{Exercise 2}
Fill in the procedure ${\verb+table-put!+}$ that inserts a
${\verb+key, value+}$ pair into the table.

\begin{verbatim}
(define (table-put! tbl key val)
  (define (insert-help node key val comp-proc)
    EXERCISE-2)
  (set-car! (cddr tbl) (insert-help (caddr tbl) key val (cadr tbl))))
\end{verbatim}

\subsection*{Exercise 3}
What is the time complexity for insertion?  How about retrieval?

\section*{Tables - Memoization}

\subsection*{Exercises 4-6}
We wish to store the result of computation on problems of smaller
size for use in future computations (assume that we use a hash table
and that we've defined ${\verb+size+}$ and ${\verb+hashfunc+}$
elsewhere).  Use this procedure to memoize ${\verb+fib+}$.  What is
the time and space complexity of ${\verb+memo-fib+}$?

\begin{verbatim}
(define (memoize f)
  (let ((table (make-table size hashfunc)))
    (lambda (x)
      (let ((previously-computed-result EXERCISE-4))
        (or previously-computed-result
            (let ((result EXERCISE-5))
              EXERCISE-6
              result))))))

(define memo-fib
  EXERCISE-7)
\end{verbatim}

\end{document}